Abstract
Neurophysiological field-potential signals consist of both arrhythmic and rhythmic patterns indicative of the fractal and oscillatory dynamics arising from likely distinct mechanisms. Here, we present a new method, namely the irregular-resampling auto-spectral analysis (IRASA), to separate fractal and oscillatory components in the power spectrum of neurophysiological signal according to their distinct temporal and spectral characteristics. In this method, we irregularly resampled the neural signal by a set of non-integer factors, and statistically summarized the auto-power spectra of the resampled signals to separate the fractal component from the oscillatory component in the frequency domain. We tested this method on simulated data and demonstrated that IRASA could robustly separate the fractal component from the oscillatory component. In addition, applications of IRASA to macaque electrocorticography and human magnetoencephalography data revealed a greater power-law exponent of fractal dynamics during sleep compared to wakefulness. The temporal fluctuation in the broadband power of the fractal component revealed characteristic dynamics within and across the eyes-closed, eyes-open and sleep states. These results demonstrate the efficacy and potential applications of this method in analyzing electrophysiological signatures of large-scale neural circuit activity. We expect that the proposed method or its future variations would potentially allow for more specific characterization of the differential contributions of oscillatory and fractal dynamics to distributed neural processes underlying various brain functions.
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References
Başar E, Başar-Eroglu C, Karakaş S, Schürmann M (2001) Gamma, alpha, delta, and theta oscillations govern cognitive processes. Int J Psychophysiol 39(2):241–248
Bassett GW Jr (1991) Equivariant, monotonic, 50 % breakdown estimators. Am Stat 45(2):135–137
Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10(3):186–198
Buzsáki G, Draguhn A (2004) Neuronal oscillations in cortical networks. Science 304(5679):1926–1929
Buzsaki G, Anastassious CA, Koch C (2012) The origin of extracellular fields and currents—EEG, ECoG, LFP and spikes. Nat Rev Neurosci 13(6):407–420
Ciuciu P, Varoquaux G, Abry P, Sadaghiani S, Kleinschmidt A (2012) Scale-free and multifractal time dynamics of fMRI signals during rest and task. Front Physiol 3:186
El Boustani S, Marre O, Béhuret S, Baudot P, Yger P, Bal T, Frégnac Y (2009) Network-state modulation of power-law frequency-scaling in visual cortical neurons. PLoS Comput Biol 5(9):e1000519
Engel AK, Gerloff C, Hilgetag CC, Nolte G (2013) Intrinsic coupling modes: multiscale interactions in ongoing brain activity. Neuron 80(4):867–886
Fransson P, Metsäranta M, Blennow M, Åden U, Lagercrantz H, Vanhatalo S (2013) Early development of spatial patterns of power-law frequency scaling in fMRI resting-state and EEG data in the newborn brain. Cereb Cortex 23(3):638–646
Freeman WJ (2007) Scale-free neocortical dynamics. Scholarpedia 2:1357
Gao J, Hu J, Tung WW (2011) Facilitating joint chaos and fractal analysis of biosignals through nonlinear adaptive filtering. PLoS One 6(9):e24331. doi:10.1371/journal.pone.0024331
González J, Gamundi A, Rial R, Nicolau MC, de Vera L, Pereda E (1999) Nonlinear, fractal, and spectral analysis of the EEG of lizard, Gallotia galloti. Am J Physiol Regul Integr Comp Physiol 277(1):R86–R93
Gray CM (1994) Synchronous oscillations in neuronal systems: mechanisms and functions. J Comput Neurosci 1(1–2):11–38
Hanslmayr S, Gross J, Klimesch W, Shapiro KL (2011) The role of alpha oscillations in temporal attention. Brain Res Rev 67(1):331–343
He BJ (2014) Scale-free brain activity: past, present, and future. Trends Cognit Sci 18(9):480–487
He BJ, Zempel JM, Snyder AZ, Raichle ME (2010) The temporal structures and functional significance of scale-free brain activity. Neuron 66(3):353–369
Hwa RC, Ferree TC (2002) Scaling properties of fluctuations in the human electroencephalogram. Phys Rev E 66(2):021901
Lakatos P, Karmos G, Mehta AD, Ulbert I, Schroeder CE (2008) Entrainment of neuronal oscillations as a mechanism of attentional selection. Science 320(5872):110–113
Liu Z, Fukunaga M, de Zwart JA, Duyn JH (2010) Large-scale spontaneous fluctuations and correlations in brain electrical activity observed with magnetoencephalography. Neuroimage 51(1):102–111
Mandelbrot BB, Van Ness JW (1968) Fractional Brownian motions, fractional noises and applications. SIAM Rev 10(4):422–437
Manning JR, Jacobs J, Fried I, Kahana MJ (2009) Broadband shifts in local field potential power spectra are correlated with single-neuron spiking in humans. J Neurosci 29(43):13613–13620
Miller KJ, Sorensen LB, Ojemann JG, den Nijs M (2009) Power-law scaling in the brain surface electric potential. PLoS Comput Biol 5(12):e1000609
Nunez PL, Srinivasan R (2006) Electrical fields of the brain: the neurophysics of EEG. Oxford University Press, Oxford
Olbrich S, Mulert C, Karch S, Trenner M, Leicht G, Pogarell O, Hegerl U (2009) EEG-vigilance and BOLD effect during simultaneous EEG/fMRI measurement. Neuroimage 45(2):319–332
Peng CK, Havlin S, Stanley HE, Goldberger AL (1995) Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5:82–87
Pereda E, Gamundi A, Rial R, Gonzalez J (1998) Non-linear behaviour of human EEG: fractal exponent versus correlation dimension in awake and sleep stages. Neurosci Lett 250(2):91–94
Rinzel J, Ermentrout GB (1998) Analysis of neural excitability and oscillations. Methods Neuronal Model 2:251–292
Robinson PA (2003) Interpretation of scaling properties of electroencephalographic fluctuations via spectral analysis and underlying physiology. Phys Rev E 67(3):032902
Schabus M, Pelikan C, Chwala-Schlegel N, Weilhart K, Roehm D, Donis J, Klimesch W (2011) Oscillatory brain activity in vegetative and minimally conscious state during a sentence comprehension task. Funct Neurol 26(1):31
Siegel M, Donner TH, Engel AK (2012) Spectral fingerprints of large-scale neuronal interactions. Nat Rev Neurosci 13(2):121–134
Wong CW, Olafsson V, Tal O, Liu TT (2013) The amplitude of the resting-state fMRI global signal is related to EEG vigilance measures. Neuroimage 83:983–990
Yamamoto YOSHIHARU, Hughson RL (1991) Coarse-graining spectral analysis: new method for studying heart rate variability. J Appl Physiol 71(3):1143–1150
Yamamoto Y, Hughson RL (1993) Extracting fractal components from time series. Phys D 68(2):250–264
Acknowledgments
The research was supported in part by NIH R01MH104402. The authors are thankful to Dr. Shao-Chin Hung for proof reading and constructive comments, to Drs. Masaki Fukunaga and Jeff Duyn for assistance in collecting the MEG data, and to Dr. Naotaka Fujii for making the macaque ECoG data publicly available.
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Wen, H., Liu, Z. Separating Fractal and Oscillatory Components in the Power Spectrum of Neurophysiological Signal. Brain Topogr 29, 13–26 (2016). https://doi.org/10.1007/s10548-015-0448-0
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DOI: https://doi.org/10.1007/s10548-015-0448-0